Over the last decades, tensor network methods have emerged as the one of
the most powerful numerical methods for tackling the many-body problem
in quantum physics. In this talk, we will review the core principles of
tensor network and their applications in condensed matter physics. We
will focus on two dimensional systems and discuss simulating strongly
correlated systems at thermal equilibrium.

In such systems, implementing efficient imaginary time evolution and
tensor network contraction proves challenging due to the requirement of
very large bond dimensions to maintain physical relevance at low
temperatures. In addition, it is essential to preserve good numerical
accuracy to avoid unphysical symmetry breakings that may hide important
physics. The solution for both issues is to incorporate non-abelian
symmetry directly at the tensor level, which yields substantial
improvements in performance and precision.

To illustrate the potential of this approach, we will present results on
the spin-1/2 Heisenberg model on the square lattice with
nearest-neighbor coupling J1 and next-nearest coupling J2 (J1-J2 model)
at finite temperature [1].

[1] O. Gauthé & F. Mila, PRL, 128, 227202 (2022)

Contact: Dragi Karevski